Semiconductor device manufacturing method

ABSTRACT

A semiconductor device manufacturing method includes applying illumination light to a photomask, and projecting diffracted light components from the photomask via a projection optical system to form a photoresist pattern on a substrate. The photomask includes a plurality of opening patterns which are arranged on each of a plurality of parallel lines at regular second intervals in a second direction and which have regular first intervals in a first direction perpendicular to the second direction. The plurality of opening patterns arranged on the adjacent ones of the plurality of parallel lines are displaced from each other half the second interval in the second direction. Moreover, the dimensions of the plurality of opening patterns and the complex amplitude transmittance of nontransparent region in the photomask are set so that three of the diffracted light components passing through the pupil of the projection optical system have equal amplitude.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is based upon and claims the benefit of priority fromprior Japanese Patent Applications No. 2008-052450, filed Mar. 3, 2008;and No. 2008-330621, filed Dec. 25, 2008, the entire contents of both ofwhich are incorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a semiconductor device manufacturingmethod. More particularly, the present invention is used to form, forexample, a bit-line contact connected to a diffusion layer of a selectedtransistor in a NAND cell unit.

2. Description of the Related Art

In a semiconductor device, forming a pattern with high density isimportant for higher integration. To this end, it has been proposed, inrelation to, for example, a NAND flash memory, to arrange a plurality ofcontact holes for bit-line contact in a staggered form (see, forexample, Japanese Patent No. 3441140).

However, opening patterns are “dense” in an oblique direction in a maskpattern for the formation of the contact holes. The reason is thatopenings (transparent regions) for the formation of the contact holesare arranged in a staggered form. Thus, an exposure allowance and thedepth of focus are reduced, and it is difficult to hold down dimensionalerrors in an exposure process. That is, the NAND flash memory requiresthe formation of a micropattern which is a dense hole pattern havingregularly arranged opening patterns and in which the holes are notorthogonally arranged in the form of a lattice. However, there hasheretofore been difficulty in highly accurately forming themicropattern.

BRIEF SUMMARY OF THE INVENTION

According to a first aspect of the present invention, there is provideda semiconductor device manufacturing method comprising: applyingillumination light from an illumination light source to a photomaskcontaining a mask pattern composed of a transparent region and anontransparent region, and projecting diffracted light components fromthe photomask on a substrate via a projection optical system to form aphotoresist pattern corresponding to the mask pattern on the substrate,wherein the mask pattern includes a plurality of opening patterns whichare the transparent regions, the centers of the opening patterns beingarranged on each of a plurality of parallel lines at regular secondintervals in a second direction, the plurality of parallel lines havingregular first intervals in a first direction and extending in the seconddirection perpendicular to the first direction, the centers of theplurality of opening patterns arranged on the adjacent ones of theplurality of parallel lines are displaced from each other half thesecond interval in the second direction; the illumination shape of theillumination light source is set so that three of the diffracted lightcomponents from the photomask pass through the pupil of the projectionoptical system; and the dimensions of the plurality of opening patternsand the complex amplitude transmittance of the nontransparent region inthe photomask are set so that the three diffracted light components haveequal amplitude.

According to a second aspect of the present invention, there is provideda semiconductor device manufacturing method comprising: applyingillumination light from an illumination light source to a photomaskcontaining a mask pattern composed of a transparent region and anontransparent region, and projecting diffracted light components fromthe photomask on a substrate via a projection optical system to form aphotoresist pattern corresponding to the mask pattern on the substrate,wherein the mask pattern includes a plurality of opening patterns whichare the transparent regions, the centers of the opening patterns beingarranged on each of a plurality of parallel lines at regular secondintervals in a second direction, the plurality of parallel lines havingregular first intervals in a first direction and extending in the seconddirection perpendicular to the first direction, the centers of theplurality of opening patterns arranged on the adjacent ones of theplurality of parallel lines are displaced from each other one third ofthe second interval in the second direction; and the illumination shapeof the illumination light source is set so that three of the diffractedlight components from the photomask pass through the pupil of theprojection optical system.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING

FIG. 1 is a plan view showing one example of a photomask according to afirst embodiment of the present invention;

FIG. 2 is a diagram showing an example of the configuration of dipoleillumination according to the first embodiment;

FIG. 3 is a plan view showing one example of contact hole patternsformed in a photoresist according to the first embodiment;

FIG. 4 is a diagram shown to explain a σ (sigma) coordinate system ofthe illumination;

FIG. 5 is a diagram shown to explain the case where verticalillumination light is used and no image is formed;

FIG. 6 is a diagram shown to explain the case where oblique illuminationlight is used and an image is formed;

FIG. 7 is a plan view of a mask pattern shown to explain the reason thatthe dipole illumination is desirable;

FIG. 8 is a diagram showing an example of the configuration of small Cillumination for radiating vertical illumination light to explain thereason that the dipole illumination is desirable;

FIG. 9 is a diagram showing the distribution of diffracted lightcomponents on a surface corresponding to the surface of a projectionlens pupil in the case where the vertical illumination light isradiated, to explain the reason that the dipole illumination isdesirable;

FIG. 10 is a diagram showing an example of the configuration of obliqueillumination for radiating oblique illumination light to explain thereason that the dipole illumination is desirable;

FIG. 11 is a diagram showing the distribution of diffracted lightcomponents on the surface corresponding to the surface of the projectionlens pupil in the case where the oblique illumination light is radiated,to explain the reason that the dipole illumination is desirable;

FIG. 12 is a diagram showing as an example the case where an image isformed on a substrate by the interference of three diffracted lightcomponents, to explain the reason that the dipole illumination isdesirable;

FIG. 13 is a diagram showing as an example the case where the maskpattern in FIG. 7 is used to form contact hole patterns in thephotoresist, to explain the reason that the dipole illumination isdesirable;

FIG. 14 is a diagram shown to explain the relation between the positionand intensity of the diffracted light in the projection lens pupil, withregard to the reason that the dipole illumination is desirable;

FIG. 15 is a diagram shown to explain the optimization of the amplitudeof interference waves;

FIG. 16 is a graph showing the relation between a mask bias and thecomplex amplitude transmittance of a attenuated phase-shift mask;

FIG. 17 is a graph showing the relation between the mask bias and theamplitude of the diffracted light;

FIG. 18 is a flowchart for finding the intensity of the diffractedlight, showing as an example the case where Kirchhoff approximate modelis not valid;

FIG. 19 is a diagram showing an example of the configuration ofquadrupole illumination;

FIG. 20 is a diagram showing the distribution of diffracted lightcomponents on a surface corresponding to the surface of a projectionlens pupil in the case where oblique illumination light is radiated, toexplain the reason that the quadrupole illumination is desirable;

FIG. 21 is a graph showing an exposure latitude obtained by thequadrupole illumination in comparison with an exposure latitude obtainedby the dipole illumination;

FIG. 22 is a diagram showing as an example the case where contact holepatterns are formed in a photoresist, to explain the reason that thequadrupole illumination is desirable;

FIGS. 23A and 23B are diagrams showing as an example the case where anindependent contact hole pattern is formed in the photoresist, toexplain the reason that the quadrupole illumination is desirable;

FIG. 24 is a diagram showing an example of the configuration of hexapoleillumination;

FIG. 25 is a diagram showing the distribution of diffracted lightcomponents on a surface corresponding to the surface of a projectionlens pupil in the case where oblique illumination light is radiated, toexplain the reason that the hexapole illumination is desirable;

FIG. 26 is a plan view showing one example of a photomask according to asecond embodiment of the present invention;

FIG. 27 is a diagram showing a triple zigzag arrangement of contactholes for bit-line contact, in a NAND flash memory as an example;

FIG. 28 is a diagram showing an example of the configuration of modifieddipole illumination according to the second embodiment;

FIG. 29 is a plan view showing one example of contact hole patternsformed in a photoresist according to the second embodiment;

FIG. 30 is a plan view of a mask pattern shown to explain the reasonthat the modified dipole illumination is desirable;

FIG. 31 is a diagram showing the distribution of diffracted lightcomponents on a surface corresponding to the surface of a projectionlens pupil in the case where vertical illumination light is radiated, toexplain the reason that the modified dipole illumination is desirable;

FIG. 32 is a diagram showing the distribution of diffracted lightcomponents on the surface corresponding to the surface of the projectionlens pupil in the case where oblique illumination light is radiated, toexplain the reason that the modified dipole illumination is desirable;

FIG. 33 is a diagram showing as an example the case where an image isformed on a substrate by the interference of three diffracted lightcomponents, to explain the reason that the modified dipole illuminationis desirable;

FIG. 34 is a diagram shown to explain the relation between the center ofthe projection lens pupil and the positions of the diffracted lightcomponents, with regard to the reason that the modified dipoleillumination is desirable;

FIG. 35 is a diagram showing wavenumber vectors of the diffracted lightcomponents with respect to the center of the projection lens pupil, toexplain the reason that the modified dipole illumination is desirable;

FIG. 36 is a diagram shown to explain the light intensities of a brightpart and dark parts, with regard to the reason that the modified dipoleillumination is desirable;

FIG. 37 is a graph shown to explain the relation between the amplitudeof the diffracted light and contrast;

FIG. 38 is a graph shown to explain the relation between ε and Δ;

FIG. 39 is a graph shown to explain the relation between ε anddiffracted light amplitude A;

FIG. 40 is a diagram showing an example of the configuration of modifiedquadrupole illumination;

FIG. 41 is a diagram showing the distribution of diffracted lightcomponents on a surface corresponding to the surface of a projectionlens pupil in the case where oblique illumination light is radiated, toexplain the reason that the modified quadrupole illumination isdesirable;

FIG. 42 is a diagram showing another distribution of the diffractedlight on the surface corresponding to the surface of the projection lenspupil in the case where the oblique illumination light is radiated, toexplain the reason that the modified quadrupole illumination isdesirable; and

FIG. 43 is a diagram showing an example of the configuration of modifiedhexapole illumination.

DETAILED DESCRIPTION OF THE INVENTION

Embodiments of the present invention will be described with reference tothe accompanying drawings. It should be noted that the drawings areschematic ones and the dimension ratios shown therein are different fromthe actual ones. The dimensions vary from drawing to drawing and so dothe ratios of dimensions. The following embodiments are directed to adevice and a method for embodying the technical concept of the presentinvention and the technical concept does not specify the material,shape, structure or configuration of components of the presentinvention. Various changes and modifications can be made to thetechnical concept without departing from the scope of the claimedinvention.

[First Embodiment]

FIG. 1 shows one example of a photomask according to a first embodimentof the present invention. It should be noted that contact holes forbit-line contact in a NAND flash memory (what is called a micropatternwhich is a dense hole pattern and in which holes are not orthogonallyarranged in the form of a lattice; for example, a double zigzagarrangement of holes in a NAND-CB layer) are formed in the casedescribed as an example in the present embodiment.

In FIG. 1, the photomask has main openings (first main openings) 11,main openings (second main openings) 12, assist openings (first assistopenings) 21, assist openings (second assist openings) 22, assistopenings (third assist openings) 23 and assist openings (fourth assistopenings) 24. These openings 11, 12, 21, 22, 23, 24 are enclosed by alight-blocking region (nontransparent region) 31. The light-blockingregion 31 is, for example, a light-blocking region in which a chromiumfilm is formed, or, for example, a semitransparent halftone phase-shiftregion in which a molybdenum silicide film is formed.

The main openings 11, 12 have the same shape and dimensions, and theassist openings 21, 22, 23, 24 have the same shape and dimensions. Theassist openings 21, 22, 23, 24 are smaller than the main openings 11,12.

The main openings 11, 12 are opening patterns (transferred patterns)corresponding to contact hole patterns for bit-line contact. Patternscorresponding to the main openings 11, 12 are formed in a photoresistafter exposure and development processes. The assist openings 21, 22,23, 24 are auxiliary patterns (non-resolution assist patterns). Patternscorresponding to the assist openings 21, 22, 23, 24 are not formed inthe photoresist after the exposure and development processes.

The plurality of main openings 11 are arranged at a pitch 2Py (secondinterval) on a straight line (first straight line) 41 extending in abit-line direction (second direction). That is, the center of each ofthe main openings 11 is located on the straight line 41. The pluralityof main openings 12 adjacent to the main openings 11 are arranged at thepitch 2Py on a straight line (second straight line) 42 extending in thebit-line direction. That is, the center of each of the main openings 12is located on the straight line 42.

The straight line 41 and the straight line 42 are parallel to eachother, and the distance (first distance (first interval) in a firstdirection (word-line direction)) between the straight line 41 and thestraight line 42 is Px. Moreover, the main openings 11 and the mainopenings 12 are displaced Py from each other in the bit-line direction.

The plurality of assist openings 21 adjacent to the main openings 11 arearranged at the pitch 2Py on a straight line (third straight line) 43extending in the bit-line direction. That is, the center of each of theassist openings 21 is located on the straight line 43. The plurality ofassist openings 22 adjacent to the main openings 12 are arranged at thepitch 2Py on a straight line (fourth straight line) 44 extending in thebit-line direction. That is, the center of each of the assist openings22 is located on the straight line 44. The plurality of assist openings23 adjacent to the assist openings 21 are arranged at the pitch 2Py on astraight line (fifth straight line) 45 extending in the bit-linedirection. That is, the center of each of the assist openings 23 islocated on the straight line 45. The plurality of assist openings 24adjacent to the assist openings 22 are arranged at the pitch 2Py on astraight line (sixth straight line) 46 extending in the bit-linedirection. That is, the center of each of the assist openings 24 islocated on the straight line 46.

The straight lines 41, 42, 43, 44, 45 and 46 are parallel to each other.The distance (first interval) between the straight line 41 and thestraight line 43 is Px. The distance between the straight line 42 andthe straight line 44 is also Px. Moreover, the distance between thestraight line 43 and the straight line 45 is Px, and the distancebetween the straight line 44 and the straight line 46 is also Px.

The assist openings 21 are displaced Py with respect to the mainopenings 11 in the bit-line direction. Likewise, the assist openings 22are displaced Py with respect to the main openings 12 in the bit-linedirection. Thus, the assist openings 21 and the assist openings 22 aredisplaced Py from each other in the bit-line direction. On the otherhand, the assist openings 23 are displaced Py from the assist openings21 in the bit-line direction. Likewise, the assist openings 24 aredisplaced Py from the assist openings 22 in the bit-line direction. Thatis, the assist openings 22, 23 are arranged at the same pitch (2Py) asthe main openings 11 in the bit-line direction. The assist openings 21,24 are also arranged at the same pitch (2Py) as the main openings 12.

It is appreciated from the above explanation that the assist openings23, the assist openings 21, the main openings 11, the main openings 12,the assist openings 22 and the assist openings 24 are arranged at thesame pitch in the oblique direction. That is, the photomask shown inFIG. 1 is increased in the periodicity in the oblique direction by theaddition of the assist openings 21, 22, 23, 24 (see, for example, U.S.application Ser. No. 11/896,871 (U.S. Publication No. 2008-0063988)).

Here, for example, it is assumed that NA=1.3, λ=193 nm, Px=80 nm andPy=90 nm when the pitch Px of the opening patterns in the word-linedirection and the pitch Py in the bit-line direction satisfy therelation in Expression (1):

$\begin{matrix}{\sqrt{P_{x}^{2} + P_{y}^{2}} < \frac{\lambda}{NA}} & (1)\end{matrix}$where NA is the numerical aperture of a projection lens, and λ is anexposure wavelength.

When a microhole pattern is to be formed under such conditions (thewavelength λ and the numerical aperture NA), the use of conventionalgeneral illumination (vertical illumination light) results ininsufficient contrast of an image to be formed on a substrate, so thatsuch conditions are vulnerable to errors in exposure or focus. It istherefore impossible to form a necessary hole pattern. There is noproblem in the case where the pitches Px, Py of the opening patterns aregreat when the size of the opening pattern on the photomask is equal toa numerical value obtained by dividing a desired dimension of the holepattern on the substrate by the magnification of the projection lens.However, the size of the opening pattern matters when the pitches Px, Pyare small.

The present embodiment enables the formation of a microhole pattern (amicropattern which is a dense hole pattern and in which holes are notorthogonally arranged in the form of a lattice) suitable for exposureunder conditions where the minimum pattern pitch of the opening patternsis λ/NA, in a photolithography technique used for the exposure of thehole patterns.

FIG. 2 shows an example of the configuration of illumination in thepresent embodiment. In the present embodiment, dipole illumination whichis modified illumination is used.

As shown in FIG. 2, the dipole illumination has a luminous region (firstluminous region) 51 and a luminous region (second luminous region) 52.These luminous regions 51, 52 are enclosed by a nonluminous region 61.

The luminous region 51 and the luminous region 52 are providedsymmetrically to each other with respect to a center 70 of illumination.That is, the luminous region 51 and the luminous region 52 have the sameshape and the same dimensions. The center of the luminous region 51 andthe center of the luminous region 52 are located symmetrically to eachother with respect to the center 70 of illumination. Moreover, theluminous region 51 and the luminous region 52 contain a point 71 (firstpoint) and a point 72 (second point), respectively. The point 71 and thepoint 72 are symmetrical to each other with respect to the center 70 ofillumination. The point 71 and the point 72 are also symmetrical to eachother with respect to a straight line 81 passing through the center 70of illumination and extending in a word-line direction (x-direction,first direction) perpendicular to the bit-line direction (y-direction,second direction). That is, the distance (dy) between the center 70 ofillumination and the point 71 is equal to the distance (dy) between thecenter 70 of illumination and the point 72.

It is ideally desirable that the center of the luminous region 51 becoincident with the point 71 and that the center of the luminous region52 be coincident with the point 72. In this case, the luminous region 51and the luminous region 52 are symmetrical to each other with respect tothe straight line 81.

In addition, it is desirable that the distance dy between the center 70of illumination and the point 71 and the distance dy between the center70 of illumination and the point 72 satisfy the relation in Expression(2) on a σ coordinate system of the illumination:

$\begin{matrix}{{dy} = {\frac{\lambda}{4{NA}}\left( {\frac{1}{P_{y}} + \frac{P_{y}}{P_{x}^{2}}} \right)}} & (2)\end{matrix}$where λ is the wavelength of the illumination light, and NA is thenumerical aperture of the projection lens through which the illuminationlight passes. The σ coordinate system will be described later.

Oblique illumination light from the above-mentioned modifiedillumination is applied to the photoresist via the above-mentionedphotomask (see FIG. 1), such that a highly accurate contact hole patternhaving controlled dimensional errors can be formed on the photoresist.

FIG. 3 shows one example of contact hole patterns formed in aphotoresist after the exposure and development processes.

As shown in FIG. 3, contact hole patterns 91, 92 are formed in aphotoresist 90. That is, patterns corresponding to the main openings 11,12 shown in FIG. 1 are formed as the contact hole patterns 91, 92 in thephotoresist 90. No patterns corresponding to the assist openings 21, 22,23, 24 shown in FIG. 1 are not formed in the photoresist 90.

Here, the above-mentioned σ coordinate system is described withreference to FIG. 4.

In FIG. 4, 111 denotes an illumination optical system, 112 denotes aphotomask, 113 denotes a projection optical system (projection lens),114 denotes a substrate (semiconductor wafer), and 115 denotes anoptical axis. The exit side numerical aperture of the illuminationoptical system 111 is sin (θ1), and the entrance side numerical apertureof the illumination optical system 113 is sin (θ2). The value σ isdefined as sin (θ1)/sin (θ2).

In the modified illumination such as the dipole illumination, the σcoordinate system is generally used with the extended definition of theσ value. In the σ coordinate system, the optical axis is determined tobe an origin, and the entrance side numerical aperture of the projectionoptical system is normalized at “1”. Therefore, an illumination positionof a T point in FIG. 4 is indicated in the σ coordinate system asfollows:(σx, σy)=(sin(θ1)/sin(θ2),0)

Described below is the reason that the highly accurate contact holepattern having controlled dimensional errors can be formed by theabove-mentioned photomask (see FIG. 1) and by an exposure method usingthe modified illumination (see FIG. 2).

When the intervals between the patterns sized on the substrate issmaller than λ/NA, the use of vertical illumination light does not allowdiffracted light components other than zero-order diffracted light toreach the substrate due to a large angle of diffraction. Thus, forexample, as shown in FIG. 5, there is no interference and no image isformed. The use of oblique illumination light enables image formationowing to the interference between zero-order diffracted light andprimary diffracted light, for example, as shown in FIG. 6.

When the oblique illumination light is used, a greater focal depth isobtained by a periodic pattern than by an independent pattern. Thus, inthe present embodiment, the assist openings 21, 22, 23, 24 shown in FIG.1 are added to provide periodicity in the whole pattern. That is, themain openings 11 and the main openings 12 shown in FIG. 1 are obliquelyarranged, so that the periodicity in the oblique direction is increasedby the addition of the assist openings 21, 22, 23, 24.

Next, the reason that the dipole illumination shown in FIG. 2 isdesirable is described. It should be noted that the followingexplanation is based on the assumption that a mask pattern (photomask)shown in FIG. 7 is used instead of the photomask shown in FIG. 1 forbrevity.

The photomask shown in FIG. 1 as a grating can be considered to producediffracted light in the same direction as the mask pattern shown in FIG.7. In FIG. 7, 121 denotes a light-blocking region, and 122 denotes anopening.

Suppose that the vertical illumination light from illumination (small σillumination) as shown in FIG. 8 is applied to the mask pattern shown inFIG. 7. That is, in the illumination in FIG. 8, a luminous region 131 isprovided in the center of illumination. In this case, diffracted lightin a surface corresponding to that of the pupil of the projection lensshows a distribution in FIG. 9. A coordinate system in FIG. 9 is the σcoordinate system in which the radius (σ value) of the projection lenspupil is normalized at “1”. That is, FIG. 9 shows the distribution ofthe diffracted light in the surface of the projection lens pupil in thecase where the mask pattern shown in FIG. 7 is Fourier-transformed.

In FIG. 9, 141 g denotes zero-order diffracted light, and 141 f denotesprimary diffracted light. The coordinate positions of four primarydiffracted light components 141 f are:(+Qx, +Qy)(+Qx, −Qy)(−Qx, +Qy)(−Qx, −Qy), whereQx=λ/(2Py×NA)

Qx=λ/(2Px×NA). In addition, λ is the wavelength of the illuminationlight, and NA is the numerical aperture of the projection lens(projection optical system). Further, in FIG. 7, the pitch of theopenings 122 in the x-direction is Px, and the pitch of the openings 122in the y-direction is Py. Moreover, 142 in FIG. 9 denotes an effectiveregion (unit circle) of the projection lens pupil, and the diffractedlight in the effective region 142 only reaches the substrate. Thus, inthe case in FIG. 9, one diffracted light (zero-order diffracted light)141 g alone reaches the substrate, so that there is no interference andno image is formed on the substrate.

Suppose that oblique illumination light from modified illumination(oblique illumination) as shown in FIG. 10 is applied to the maskpattern shown in FIG. 7. The position (a luminous region 132) of theoblique illumination light is properly shifted (shift amount σs) in ay-axis direction, such that three diffracted light components 141 a, 141b, 141 c can be positioned in the effective region 142 of the projectionlens pupil, for example, as shown in FIG. 11. Therefore, the threediffracted light components 141 a, 141 b, 141 c reach the substratethrough the projection lens, so that interference is produced and animage can be formed on the substrate.

In the example shown in FIG. 12, an image (see FIG. 3) corresponding tothe openings 122 in FIG. 7 is formed on the substrate by theinterference of the three diffracted light components 141 a, 141 b, 141c shown in FIG. 11.

As shown in FIG. 12, one-dimensional interference fringes 151 areproduced on the substrate due to the interference between the diffractedlight 141 a and the diffracted light 141 b. Likewise, interferencefringes 152 are produced on the substrate due to the interferencebetween the diffracted light 141 b and the diffracted light 141 c, andinterference fringes 153 are produced on the substrate due to theinterference between the diffracted light 141 c and the diffracted light141 a. It should be noted that full lines indicate the peaks of thebright parts of the interference fringes and that broken lines indicatethe peaks of the dark parts of the interference fringes. The lightintensity is particularly high at parts 155 where the bright parts ofthe three interference fringes 151, 152, 153 overlap. Therefore, asshown in FIG. 13, when a positive photoresist 90 a is used, contact holepatterns 93 are formed at the positions corresponding to the parts 155.

In addition, FIG. 13 shows the example in which the mask pattern shownin FIG. 7 is used. In the case where the photomask as shown in FIG. 1 isused, an image is formed on the substrate with image intensitycorresponding to the sizes of the main openings 11, 12 and the assistopenings 21, 22, 23, 24, so that contact hole patterns 91, 92corresponding to the main openings 11, 12 can only be formed in thephotoresist 90 (see FIG. 3).

Here, the relation between the position and intensity of the diffractedlight in the projection lens pupil is described.

In FIG. 14, the diffracted light 141 a is a light traveling straight inthe mask, that is, zero-order diffracted light. The diffracted lightcomponents 141 b, 141 c are primary diffracted light components. In acommonly used binary mask or attenuated phase-shift mask, the diffractedlight components 141 b, 141 c have common amplitude and phase. When themask pattern is formed by the binary mask or the attenuated phase-shiftmask, the amplitude (intensity) A of the diffracted light 141 a in theprojection lens pupil and the amplitudes B, C of the diffracted lightcomponents 141 b, 141 c are represented by Expressions (3), (4):

$\begin{matrix}{A = {\gamma + {2\left( {1 - \gamma} \right)ɛ_{x}ɛ_{y}}}} & (3) \\{B = {C = {2\left( {1 - \gamma} \right)\frac{\sin\left( {ɛ_{x}\pi} \right)}{\pi}\frac{\sin\left( {ɛ_{y}\pi} \right)}{\pi}}}} & (4)\end{matrix}$where γ (a negative value corresponds to the phase-shift mask and 0corresponds to the binary mask) is the complex amplitude transmittanceof a mask light-blocking member (light-blocking region).

<Optimization of Illumination Position>

The shift amount σs of the illumination is set to satisfy Expression(5):

$\begin{matrix}{\sigma_{s} = {\frac{\lambda}{4{NA}}\left( {\frac{1}{P_{y}} + \frac{P_{y}}{P_{x}^{2}}} \right)}} & (5)\end{matrix}$

In this case, the distances a, b, c of the three diffracted lightcomponents 141 a, 141 b, 141 c from the center of the pupil are equal toeach other. As a result, there is no defocus dependency of theinterference fringes on the substrate to be calculated later. That is,the focal depth is great enough.

Furthermore, the illumination should be axially symmetrical so that animage may not be positioned out of focus. Hence, the dipole illuminationshown in FIG. 2 in which the illumination regions are axiallysymmetrically arranged is desirable.

<Optimization of Interference Wave Amplitude>

The intensity distribution I (x, y) of an interference wave formed onthe substrate is represented by Expression (6):I(x,y)=|A exp(−ik _(a) ·x)+B exp(−ik _(b) ·x)+C exp(−ik _(c) ·x)|²   (6)where k_(a), k_(b), k_(c) are wavenumber vectors of the diffracted lightcomponents 141 a, 141 b, 141 c, and x is a position vector.

Expressions (3), (4) are substituted for Expression (6), and the resultis expanded to obtain Expression (7):

$\begin{matrix}{{{I\left( {x,y} \right)} = {\left( {A^{2} + {2B^{2}}} \right) + {2{AB}\;{\cos\left( {{\frac{\sqrt{3}}{2}{xS}} - {\frac{3}{2}{yS}}} \right)}} + {2{AB}\;{\cos\left( {{\frac{\sqrt{3}}{2}{xS}} + {\frac{3}{2}{yS}}} \right)}} + {2B^{2}{\cos\left( {\sqrt{3}{xS}} \right)}}}}\mspace{79mu}{{{where}\mspace{14mu} S} = {\frac{2\pi}{\lambda}\sin\;{\theta.}}}} & (7)\end{matrix}$where θ is an angle between the traveling direction of each diffractedlight and the normal to the surface of the substrate. Moreover, thefirst term on the right side of Expression (7) is a uniform component.The second term is an interference wave produced by the interferencebetween the diffracted light 141 a and the diffracted light 141 b. Thethird term is an interference wave produced by the interference betweenthe diffracted light 141 a and the diffracted light 141 c. The fourthterm is an interference wave produced by the interference between thediffracted light 141 b and the diffracted light 141 c.

Here, illumination is provided to satisfy the conditions in Expression(5), and thus no component dependent on z appears in Expression (7).This means that the interference fringes are not affected by defocus inthe vicinity of the best focus.

The light intensities in a bright part 156 and two kinds of dark parts157, 158 shown in FIG. 15 are explained in order to consider thecontrast of the interference wave. The light intensities in the brightpart 156 and the two kinds of dark parts 157, 158 are provided byExpressions (8), (9), (10). It should be noted that there are aplurality of bright parts and dark parts in addition to the parts shown,and these parts have the common intensity owing to the symmetry. Theintensity in each part can be found by Expression (7).

$\begin{matrix}\begin{matrix}{{{Intensity}\mspace{14mu}{of}\mspace{14mu}{the}\mspace{14mu}{bright}\mspace{14mu}{part}\mspace{14mu}(156)\mspace{14mu} I_{0}} = {I\left( {0,0} \right)}} \\{= {A^{2} + {4B^{2}} + {4{AB}}}}\end{matrix} & (8) \\{{{Intensity}\mspace{14mu}{of}\mspace{14mu}{the}\mspace{14mu}{dark}\mspace{14mu}{part}\mspace{14mu}(157)\mspace{14mu} I_{1}} = {{I\left( {\frac{\pi}{\sqrt{3}S},\frac{\pi}{3S}} \right)} = A^{2}}} & (9) \\{{{Intensity}\mspace{14mu}{of}\mspace{14mu}{the}\mspace{14mu}{dark}\mspace{14mu}{part}\mspace{14mu}(158)\mspace{14mu} I_{2}} = {{I\left( {0,\frac{2\pi}{3S}} \right)} = \left( {A - {2B}} \right)^{2}}} & (10)\end{matrix}$

In the case in FIG. 15, two kinds of contrasts can be defined. Thismeans, as indicated in Expressions (11), (12), a contrast C₁ alongbright part 156-dark part 157-bright part 156, and a contrast C₂ alongbright part 156-dark part 158-bright part 156.

$\begin{matrix}{C_{1} = {\frac{I_{0} - I_{1}}{I_{0} + I_{1}} = \frac{2{B\left( {A + B} \right)}}{A^{2} + {2B^{2}} + {2{AB}}}}} & (11) \\{C_{2} = {\frac{I_{0} - I_{2}}{I_{0} + I_{2}} = \frac{8{AB}}{{2A^{2}} + {8B^{2}}}}} & (12)\end{matrix}$

Suppose conditions where the contrasts C₁, C₂ are maximized. First, thevalue of the contrast C₁ along bright part 156-dark part 157-bright part156 is maximized under the condition where the intensity in the darkpart 157 is 0, that is, in the case where “A=0” in accordance withExpression (9). At this point, “C₁=1” but “C₂=0”, so that a desiredimage cannot be formed. On the other hand, the value of the contrast C₂along bright part 156-dark part 158-bright part 156 is maximized underthe condition where the intensity in the dark part 158 is 0, that is, inthe case where “A=2B” in accordance with Expression (10). At this point,“C₁=0.6” and “C₂=1”. This means that the intensity of the contrast C₁ isnot enough.

Thus, if the condition where “C₁=C₂” is an optimum condition, this isachieved when the intensity in the dark part 157 is equal to theintensity in the dark part 158. Therefore, this proves to be correspondto the case where “A=B” in accordance with Expressions (9), (10). Inthis case, “C₁=C₂=0.8”.

Consequently, it is apparent that a desirable state of image formationis obtained when the amplitudes A, B, C of the three diffracted lightcomponents 141 a, 141 b, 141 c used for image formation are equal toeach other.

<Optimization of Mask Bias and Light-blocking Portion AmplitudeTransmittance>

The desirable state of image formation is obtained when “A=B”, in otherwords, when Expression (13) is valid, in accordance with Expressions(3), (4), (5).

$\begin{matrix}{{\gamma + {2\left( {1 - \gamma} \right)ɛ_{x}ɛ_{y}}} = {2\left( {1 - \gamma} \right)\frac{\sin\left( {ɛ_{x}\pi} \right)}{\pi}\frac{\sin\left( {ɛ_{y}\pi} \right)}{\pi}}} & (13)\end{matrix}$

Expression (14) is the transformation of Expression (13).

$\begin{matrix}{\gamma = \frac{{2\pi^{2}ɛ_{x}ɛ_{y}} - {2{\sin\left( {ɛ_{x}\pi} \right)}{\sin\left( {ɛ_{y}\pi} \right)}}}{{2\pi^{2}ɛ_{x}ɛ_{y}} - 1 - {2{\sin\left( {ɛ_{x}\pi} \right)}{\sin\left( {ɛ_{y}\pi} \right)}}}} & (14)\end{matrix}$

That is, the desirable state of image formation is obtained when a maskbias (ε) and the complex amplitude transmittance (γ) of the attenuatedphase-shift mask satisfy the predetermined relation represented byExpression (14).

Here, suppose that “εx=εy=ε” for simplicity, Expression (14) isrepresented by Expression (15):

$\begin{matrix}{\gamma = \frac{{2\pi^{2}ɛ^{2}} - {2{\sin^{2}({ɛ\pi})}}}{{2\pi^{2}ɛ^{2}} - 1 - {2{\sin^{2}({ɛ\pi})}}}} & (15)\end{matrix}$

FIG. 16 shows the relation between the mask bias (ε) and the complexamplitude transmittance (γ) of the attenuated phase-shift mask. Negative“γ” represents the situation in which the phase of light passing throughthe halftone region (mask light-blocking member) is displaced 180degrees with respect to light passing a light transmitting region. Allthe situations on this curve satisfy the condition in which thediffracted light intensities are equal to each other.

FIG. 17 shows the relation between the mask bias (the dimension ε of theopening on the mask) and diffracted light amplitude A. It is appreciatedfrom this graph that the image is bright when the mask bias is high andwhen the complex amplitude transmittance of the mask light-blockingmember is negatively high. While the brightness of the image has to beset in accordance with, for example, a desired throughput, resistsensitivity and the stability of laser luminance, the brightness of theimage can be set by properly selecting a combination of a mask bias andcomplex amplitude transmittance.

As described above, according to the present embodiment, the photomaskhaving the assist openings 21, 22, 23, 24 as shown in FIG. 1 is used,and the dipole illumination having the luminous regions 51, 52 as shownin FIG. 2 is used. Thus, the highly accurate contact hole patterns 91,92 having controlled dimensional errors as shown in FIG. 3 can be formedeven if the pattern is miniaturized.

Consequently, when the photomask and modified illumination describedabove are applied to the manufacture of a semiconductor device (exposureof hole patterns), for example, contact holes for bit-line contact to beconnected to a diffusion layer of a selected transistor in a NAND cellunit can be highly accurately formed in a NAND flash memory.

In addition, in the case of the first embodiment described above, theamplitudes of the diffracted light components indicated in Expressions(3), (4) are derived on the basis of a model which determines that amask pattern is formed of an infinitely thin film, that is, on the basisof Kirchhoff approximate model. It has recently come to be known thatthe Kirchhoff approximate model is not valid due to the thickness of themask under the condition where the minimum dimensions of a mask patternare substantially equal to or less than a wavelength. In this case, theintensity of a diffracted light cannot be represented by a simpleexpression such as Expressions (3), (4) and can be found by numericallysolving a Maxwell's equation. That is, a condition where the intensitiesof three diffracted light components are equal to each other is found byrepetitive calculations in such a manner as to change the complexamplitude transmittance of the mask and the dimensions of the contacthole pattern, for example, as shown in FIG. 18.

In particular, when there is no need for a calculation that takes intoaccount the influence of the thickness of the mask, the calculationshown in FIG. 18 has only to be performed using transmittance instead ofthe optical constant of a attenuated film.

Furthermore, four assist openings are provided in the example describedin the above embodiment. This is not limitation. For example, six ormore rows of assist openings may be provided.

Still further, the shape of the main openings and assist openings is notexclusively square and may be, for example, rectangular, circular orelliptic.

Further yet, the shape of the luminous regions of the modifiedillumination is not exclusively circular and may be, for example,elliptic.

Further yet, the modified illumination is not exclusively the dipoleillumination and may be, for example, quadrupole illumination.

FIG. 19 shows an example of the configuration of quadrupole illuminationsuitably used for the formation of contact holes for bit-line contact ina NAND flash memory (e.g., a double zigzag arrangement of holes in aNAND-CB layer).

As shown in FIG. 19, the quadrupole illumination which is modifiedillumination has a luminous region (first luminous region) 251, aluminous region (second luminous region) 252, a luminous region (thirdluminous region) 253 and a luminous region (fourth luminous region) 254.These luminous regions 251, 252, 253, 254 are enclosed by a nonluminousregion 261.

The luminous regions 251, 252, 253, 254 are provided at positions(regions) in crossing directions substantially symmetrically in the x-and y-directions with respect to a center 270 of illumination. That is,the luminous regions 251, 252, 253, 254 have the same shape and the samedimensions. For example, the distance (σ) between the center 270 ofillumination and a point contained in the luminous region 251 isprovided by Expressions (16), (17), (18).

$\begin{matrix}{\sigma_{x} = \frac{\lambda}{2{NAP}_{x}}} & (16) \\{\sigma_{y} = {\frac{\lambda}{4{NA}}\left( {\frac{1}{P_{y}} - \frac{P_{y}}{P_{x}^{2}}} \right)}} & (17) \\{\sigma = {\frac{\lambda}{4{NA}}\left( {\frac{1}{P_{y}} + \frac{P_{y}}{P_{x}^{2}}} \right)}} & (18)\end{matrix}$where NA is the numerical aperture of the projection lens, λ is anexposure wavelength, Px is the pitch of the opening patterns in theword-line direction, and Py is the pitch of the opening patterns in thebit-line direction.

In this connection, the distance (σ) between the center 270 ofillumination and the point contained in the luminous region 251 isprovided by σx, σy. The distance (σ) between the center 270 ofillumination and a point contained in the luminous region 252 isprovided by σx, −σy. The distance (σ) between the center 270 ofillumination and a point contained in the luminous region 253 isprovided by −σx, σy. The distance (σ) between the center 270 ofillumination and a point contained in the luminous region 254 isprovided by −σx, −σy.

In addition, it is ideally desirable that the center of the luminousregion 251 be coincident with the point contained therein, the center ofthe luminous region 252 be coincident with the point contained therein,the center of the luminous region 253 be coincident with the pointcontained therein, and the center of the luminous region 254 becoincident with the point contained therein. In this case, the distances(σ) of the luminous regions 251, 252, 253, 254 from the center 270 ofillumination are equal to each other.

That is, the shape of the quadrupole illumination having the luminousregions 251, 252, 253, 254 in the directions prescribed by the x- andy-directions is set so that three of the diffracted light componentsfrom the photomask pass through the projection lens pupil. In the caseof the mask pattern shown in FIG. 7, this quadrupole illuminationpermits three diffracted light components 241 a, 241 b, 241 c to belocated in each of effective regions 242 a, 242 b, 242 c, 242 d of theprojection lens pupil, for example, as shown in FIG. 20. Thus, the threediffracted light components 241 a, 241 b, 241 c reach the substratethrough the projection lens, so that the interference (dark part peaksand bright part peaks in interference fringes) as shown in FIG. 15 iscaused, and an image can be formed on the substrate.

FIG. 21 shows an exposure latitude obtained by the quadrupoleillumination having the luminous regions 251, 252, 253, 254 incomparison with an exposure latitude obtained by the dipole illuminationhaving the luminous regions 51, 52 (see FIG. 2). In addition, a requiredmargin indicated in the graph is the standard by which an exposureamount and defocus is determined to be unallowable in accordance withthe deviation of the dimensions of an actually formed contact holepattern from desired dimensions of a contact hole pattern formed when apredetermined mask pattern is exposed in a certain exposure amount andwith a certain focus.

As apparent from this graph, the dipole illumination (indicated by ▪)also makes it possible to obtain an exposure latitude (exposure amountvariation margin (EL) and depth of focus (DOF)) substantially equal tothat in the case of the quadrupole illumination (indicated by □).

As a result, when the photomask shown in FIG. 1 is used, the contacthole patterns 91, 92 are formed in the photoresist 90, for example, asshown in FIG. 22.

Furthermore, when the quadrupole illumination is employed, it ispossible to form in the photoresist 90 randomly arranged independentcontact hole patterns 190 in addition to periodic dense hole patternssuch as the contact hole patterns 91, 92.

In the case of the quadrupole illumination having the luminous regions251, 252, 253, 254, symmetry when rotated 90 degrees is moresatisfactory than in the case of the dipole illumination having theluminous regions 51, 52. Thus, for example, as shown in FIG. 23A, anopening 222 of the photomask is corrected to be slightly horizontallylong, so that the independent contact hole pattern 190 can be formedinto a satisfactory circular shape, for example, as shown in FIG. 23B.In addition, 221 denotes a light-blocking region of the photomask.

Thus, in the case where a contact hole for bit-line contact in a NANDflash memory is to be formed, the use of a photomask containing anopening pattern for the formation of an independent contact hole makesit possible not only to form the contact hole for bit-line contact butalso to simultaneously form, for example, an independent contact holefor peripheral circuits different in period from the contact hole forbit-line contact.

Furthermore, the illumination is not limited to the dipole illuminationand quadrupole illumination described above. It is also possible to usehexapole illumination having the luminous regions (fifth and sixthluminous regions) 51, 52 and the luminous regions (first to fourthluminous regions) 251, 252, 253, 254, for example, as shown in FIG. 24.The luminous regions 51, 52, 251, 252, 253, 254 have the same shape andthe same dimensions, and are enclosed by the nonluminous region 261.

The luminous regions 51, 52, 251, 252, 253, 254 are provided atpositions symmetrical to each other in the y-direction and at positions(regions) in crossing directions substantially symmetrically in the x-and y-directions with respect to the center of illumination. Forexample, the distance (σ) between the center of illumination and a pointcontained in the luminous region 251 is provided by Expressions (19),(20). The distance (σ) between the center of illumination and a pointcontained in the luminous region 51 is provided by Expression (21).

$\begin{matrix}{\sigma_{x} = \frac{\lambda}{2{NAP}_{x}}} & (19) \\{\sigma_{y} = {\frac{\lambda}{4{NA}}\left( {\frac{1}{P_{y}} - \frac{P_{y}}{P_{x}^{2}}} \right)}} & (20) \\{\sigma = {\frac{\lambda}{4{NA}}\left( {\frac{1}{P_{y}} + \frac{P_{y}}{P_{x}^{2}}} \right)}} & (21)\end{matrix}$where that NA is the numerical aperture of the projection lens, λ is anexposure wavelength, Px is the pitch of the opening patterns in theword-line direction, and Py is the pitch of the opening patterns in thebit-line direction.

In this connection, the distance (σ) between the center of illuminationand the point contained in the luminous region 251 is provided by σx,σy. The distance (σ) between the center of illumination and a pointcontained in the luminous region 252 is provided by σx, −σy. Thedistance (σ) between the center of illumination and a point contained inthe luminous region 253 is provided by −σx, σy. The distance (σ) betweenthe center of illumination and a point contained in the luminous region254 is provided by −σx, −σy. The distance (σ) between the center ofillumination and the point contained in the luminous region 51 isprovided by σy. The distance (σ) between the center of illumination anda point contained in the luminous region 52 is provided by −σy.

In addition, it is ideally desirable that the center of the luminousregion 51 be coincident with the point contained therein, the center ofthe luminous region 52 be coincident with the point contained therein,the center of the luminous region 251 be coincident with the pointcontained therein, the center of the luminous region 252 be coincidentwith the point contained therein, the center of the luminous region 253be coincident with the point contained therein, and the center of theluminous region 254 be coincident with the point contained therein. Inthis case, the distances (σ) of the luminous regions 51, 52, 251, 252,253, 254 from the center of illumination are equal to each other.

That is, the shape of the hexapole illumination having the luminousregions 51, 52, 251, 252, 253, 254 is set so that three of thediffracted light components from the photomask pass through theprojection lens pupil. In the case of the mask pattern shown in FIG. 7,this hexapole illumination permits three diffracted light components 241a, 241 b, 241 c to be located in each of the effective regions 242 a,242 b, 242 c, 242 d, 242 e 242 f of the projection lens pupil, forexample, as shown in FIG. 25. Thus, the three diffracted lightcomponents 241 a, 241 b, 241 c reach the substrate through theprojection lens, so that the interference, for example, as shown in FIG.15 is caused, and an image can be formed on the substrate. That is,similarly to the quadrupole illumination, in the case where a contacthole for bit-line contact in a NAND flash memory is to be formed, theuse of a photomask containing an opening pattern for the formation of anindependent contact hole makes it possible not only to form the contacthole for bit-line contact but also to simultaneously form, for example,an independent contact hole for peripheral circuits different in periodfrom the contact hole for bit-line contact.

[Second Embodiment]

FIG. 26 shows one example of a photomask according to a secondembodiment of the present invention. It should be noted that contactholes for bit-line contact in a NAND flash memory (what is called amicropattern which is a dense hole pattern and in which holes are notorthogonally arranged in the form of a lattice; for example, a triplezigzag arrangement of holes in a NAND-CB layer) are formed in the casedescribed as an example in the present embodiment.

That is, in the present embodiment, for example, as shown in FIG. 27,contact holes CB for bit-line contact connected to bit lines BL of ahalf-pitch (HPnm) width are arranged in three rows (triple zigzagarrangement) in a staggered form in a NAND flash memory. In this case,the contact holes CB are disposed at the same position in the bit linesBL 6 HPnm away from each other. This enables the highly accuratearrangement (formation) of the contact holes CB for bit-line contact inthe NAND flash memory having a reduced thickness of the bit line BL anda reduced pitch between the bit lines BL.

In FIG. 26, the photomask has main openings (first main openings) 311,main openings (second main openings) 312, main openings (third mainopenings) 313, assist openings (first assist openings) 321, assistopenings (second assist openings) 322, assist openings (third assistopenings) 323, assist openings (fourth assist openings) 324, assistopenings (fifth assist openings) 325 and assist openings (sixth assistopenings) 326. These openings 311, 312, 313, 321, 322, 323, 324, 325,326 are enclosed by a light-blocking region (nontransparent region) 331.The light-blocking region 331 is, for example, a light-blocking regionin which a chromium film is formed, or, for example, a semitransparenthalftone phase-shift region in which a molybdenum silicide film isformed.

The main openings 311, 312, 313 have the same shape and dimensions, andthe assist openings 321, 322, 323, 324, 325, 326 have the same shape anddimensions. The assist openings 321, 322, 323, 324, 325, 326 are smallerthan the main openings 311, 312, 313.

The main openings 311, 312, 313 are opening patterns (transferredpatterns) corresponding to contact hole patterns for bit-line contact.Patterns corresponding to the main openings 311, 312, 313 are formed ina photoresist after exposure and development processes. The assistopenings 321, 322, 323, 324, 325, 326 are auxiliary patterns(non-resolution assist patterns). Patterns corresponding to the assistopenings 321, 322, 323, 324, 325, 326 are not formed in the photoresistafter the exposure and development processes.

The plurality of main openings 311 are arranged at a pitch Px (secondinterval) on a straight line (first straight line) 341 extending in abit-line direction (second direction). That is, the center of each ofthe main openings 311 is located on the straight line 341. The pluralityof main openings 312 adjacent to the main openings 311 are arranged atthe pitch Px on a straight line (second straight line) 342 extending inthe bit-line direction. That is, the center of each of the main openings312 is located on the straight line 342. The plurality of main openings313 adjacent to the main openings 312 are arranged at the pitch Px on astraight line (third straight line) 343 extending in the bit-linedirection. That is, the center of each of the main openings 313 islocated on the straight line 343.

The straight line 341, the straight line 342 and the straight line 343are parallel to each other, and the distance (first distance (firstinterval) in a first direction (word-line direction)) between thestraight line 341, the straight line 342 and the straight line 343 isPy. Moreover, the main openings 311, the main openings 312 and the mainopenings 313 are displaced Px/3 (2HPnm) from each other in the bit-linedirection.

The plurality of assist openings 321 adjacent to the main openings 311are arranged at the pitch Px on a straight line (fourth straight line)344 extending in the bit-line direction. That is, the center of each ofthe assist openings 321 is located on the straight line 344. Theplurality of assist openings 322 adjacent to the main openings 313 arearranged at the pitch Px on a straight line (fifth straight line) 345extending in the bit-line direction. That is, the center of each of theassist openings 322 is located on the straight line 345. The pluralityof assist openings 323 adjacent to the assist openings 321 are arrangedat the pitch Px on a straight line (sixth straight line) 346 extendingin the bit-line direction. That is, the center of each of the assistopenings 323 is located on the straight line 346. The plurality ofassist openings 324 adjacent to the assist openings 322 are arranged atthe pitch Px on a straight line (seventh straight line) 347 extending inthe bit-line direction. That is, the center of each of the assistopenings 324 is located on the straight line 347. The plurality ofassist openings 325 adjacent to the assist openings 323 are arranged atthe pitch Px on a straight line (eighth straight line) 348 extending inthe bit-line direction. That is, the center of each of the assistopenings 325 is located on the straight line 348. The plurality ofassist openings 326 adjacent to the assist openings 324 are arranged atthe pitch Px on a straight line (ninth straight line) 349 extending inthe bit-line direction. That is, the center of each of the assistopenings 326 is located on the straight line 349.

The straight lines 341, 342, 343, 344, 345, 346, 347, 348 and 349 areparallel to each other. The distance (first interval) between thestraight line 341 and the straight line 344 is Py, and the distancebetween the straight line 343 and the straight line 345 is also Py.Further, the distance between the straight line 344 and the straightline 346 is Py, and the distance between the straight line 345 and thestraight line 347 is also Py. Moreover, the distance between thestraight line 346 and the straight line 348 is Py, and the distancebetween the straight line 347 and the straight line 349 is also Py.

In addition, the assist openings 322, 325 are arranged at the same pitch(Px) as the main openings 311 in the bit-line direction. The assistopenings 323, 324 are also arranged at the same pitch (Px) as the mainopenings 312. The assist openings 321, 326 are also arranged at the samepitch (Px) as the main openings 313. That is, the assist openings 321,326, the assist openings 323, 324 and the assist openings 322, 325 aredisplaced Px/3 from each other in the bit-line direction.

It is appreciated from the above explanation that the assist openings325, the assist openings 323, the assist openings 321, the main openings311, the main openings 312, the main openings 313, the assist openings322, the assist openings 324 and the assist openings 326 are arranged atthe same pitch in the oblique direction. That is, the photomask shown inFIG. 26 is increased in the periodicity in the oblique direction by theaddition of the assist openings 321, 322, 323, 324, 325, 326.

Here, for example, it is assumed that NA=1.3, λ=193 nm, Px=110 nm andPy=110 nm when the pitch Py of the opening patterns in the word-linedirection and the pitch Px in the bit-line direction satisfy therelation in Expression (22):

$\begin{matrix}{\sqrt{\left( \frac{P_{x}}{3} \right)^{2} + P_{y}^{2}} < \frac{\lambda}{NA}} & (22)\end{matrix}$where NA is the numerical aperture of a projection lens, and λ is anexposure wavelength.

When a microhole pattern is to be formed under such conditions (thewavelength λ and the numerical aperture NA), the use of conventionalgeneral illumination (vertical illumination light) results ininsufficient contrast of an image to be formed on a substrate, so thatsuch conditions are vulnerable to errors in exposure or focus. It istherefore impossible to form a necessary hole pattern. There is noproblem in the case where the pitches Px, Py of the opening patterns aregreat when the size of the opening pattern on the photomask is equal toa numerical value obtained by dividing a desired dimension of the holepattern on the substrate by the magnification of the projection lens.However, the size of the opening pattern matters when the pitches Px, Pyare small.

The present embodiment enables the formation of a microhole pattern (amicropattern which is a dense hole pattern and in which holes are notorthogonally arranged in the form of a lattice) suitable for exposureunder conditions where the minimum pattern pitch of the opening patternsis λ/NA, in a photolithography technique used for the exposure of thehole patterns.

FIG. 28 shows an example of the configuration of illumination in thepresent embodiment. In the present embodiment, modified dipoleillumination which is modified illumination is used.

As shown in FIG. 28, the modified dipole illumination has a luminousregion (first luminous region) 451 and a luminous region (secondluminous region) 452. These luminous regions 451, 452 are enclosed by anonluminous region 461.

The luminous region 451 and the luminous region 452 are provided atsymmetrical positions prescribed by the x- and y-directions with respectto a center 470 of illumination. That is, the luminous region 451 andthe luminous region 452 have the same shape and the same dimensions. Thecenter of the luminous region 451 and the center of the luminous region452 are located symmetrically to each other with respect to the center470 of illumination. In this case, the distance (σ) between the center470 of illumination and the center of the luminous region 451 is equalto the distance between the center 470 of illumination and the center ofthe luminous region 452. It is ideally desirable that the center of theluminous region 451 be coincident with a point contained therein andthat the center of the luminous region 452 be coincident with a pointcontained therein.

In addition, the distance a between the center 470 of illumination andthe contained points provided by Expressions (23), (24):

$\begin{matrix}{\sigma_{x} = {\frac{\lambda}{18{NA}}\left( {\frac{9}{P_{x}} + \frac{2P_{x}}{P_{y}^{2}}} \right)}} & (23) \\{\sigma_{y} = {- \frac{\lambda}{6P_{y}{NA}}}} & (24)\end{matrix}$where λ is the wavelength of the illumination light, and NA is thenumerical aperture of the projection lens through which the illuminationlight passes.

Oblique illumination light from the above-mentioned modifiedillumination is applied to the photoresist via the above-mentionedphotomask (see FIG. 26), such that a highly accurate contact holepattern having controlled dimensional errors can be formed on thephotoresist.

FIG. 29 shows one example of contact hole patterns formed in aphotoresist after the exposure and development processes.

As shown in FIG. 29, contact hole patterns 491, 492, 493 are formed in aphotoresist 490. That is, patterns corresponding to the main openings311, 312, 313 shown in FIG. 26 are formed as the contact hole patterns491, 492, 493 in the photoresist 490. No patterns corresponding to theassist openings 321, 322, 323, 324, 325, 326 shown in FIG. 26 are notformed in the photoresist 490.

Described below is the reason that the highly accurate contact holepattern having controlled dimensional errors can be formed by theabove-mentioned photomask (see FIG. 26) and by an exposure method usingthe modified illumination (see FIG. 28).

When the intervals between the patterns sized on the substrate issmaller than λ/NA, the use of vertical illumination light as in small σillumination does not allow diffracted light components other thanzero-order diffracted light to reach the substrate due to a large angleof diffraction. Thus, for example, as shown in FIG. 5, there is nointerference and no image is formed. The use of oblique illuminationlight as in the modified dipole illumination enables image formationowing to the interference between zero-order diffracted light andprimary diffracted light, for example, as shown in FIG. 6.

When the oblique illumination light is used, a greater focal depth isobtained by a periodic pattern than by an independent pattern. Thus, inthe present embodiment, the assist openings 321, 322, 323, 324, 325, 326shown in FIG. 26 are added to provide periodicity in the whole pattern.That is, the main openings 311, 312, 313 shown in FIG. 26 are obliquelyarranged, so that the periodicity in the oblique direction is increasedby the addition of the assist openings 321, 322, 323, 324, 325, 326.

Next, the reason that the modified dipole illumination shown in FIG. 28is desirable is described. It should be noted that the followingexplanation is based on the assumption that a mask pattern (photomask)shown in FIG. 30 is used instead of the photomask shown in FIG. 26 forbrevity.

The photomask shown in FIG. 26 as grating can be considered to produce adiffracted light in the same direction as the mask pattern shown in FIG.30. In FIG. 30, 521 denotes a light-blocking region, and 522 denotes anopening.

Suppose that the vertical illumination light from illumination (small σillumination) as shown in FIG. 8 is applied to the mask pattern shown inFIG. 30. That is, in the illumination in FIG. 8, a luminous region 131is provided in the center of illumination. In this case, a diffractedlight in a surface corresponding to that of the pupil of the projectionlens shows a distribution in FIG. 31. A coordinate system in FIG. 31 isa coordinate system which is normalized by the numerical aperture NA ofthe projection lens. That is, FIG. 31 shows the distribution of thediffracted light in the surface of the projection lens pupil in the casewhere the mask pattern shown in FIG. 30 is Fourier-transformed.

In FIG. 31, 541 g denotes zero-order diffracted light, and 541 f denotes1st-order diffracted light. Further, in FIG. 30, the pitch of theopenings 522 in the x-direction is Px, and the pitch of the openings 522in the y-direction is Py. Moreover, 542 in FIG. 31 denotes an effectiveregion (unit circle) of the projection lens pupil, and the diffractedlight in the effective region 542 only reaches the substrate. Thus, inthe case in FIG. 31, one diffracted light (zero-order diffracted light)541 g alone reaches the substrate, so that there is no interference andno image is formed on the substrate.

Suppose that oblique illumination light from modified illumination(oblique illumination) as shown in FIG. 10 is applied to the maskpattern shown in FIG. 30. The position (a luminous region 132) of theoblique illumination light is properly shifted (shift amounts σx, σy) ina x- and y-axis directions, such that three diffracted light components541 a, 541 b, 541 c can be positioned in the effective region 542 of theprojection lens pupil, for example, as shown in FIG. 32. Therefore, thethree diffracted light components 541 a, 541 b, 541 c reach thesubstrate through the projection lens, so that interference is producedand an image is formed on the substrate.

In the example shown in FIG. 33, an image corresponding to the openings522 in FIG. 30 is formed on the substrate by the interference of thethree diffracted light components 541 a, 541 b, 541 c shown in FIG. 32.

As shown in FIG. 33, one-dimensional interference fringes 551 areproduced on the substrate due to the interference between the diffractedlight 541 a (A) and the diffracted light 541 b (B). Likewise,interference fringes 552 are produced on the substrate due to theinterference between the diffracted light 541 b (B) and the diffractedlight 541 c (C), and interference fringes 553 are produced on thesubstrate due to the interference between the diffracted light 541 c (C)and the diffracted light 541 a (A). It should be noted that full linesindicate the peaks of the bright parts of the interference fringes andthat broken lines indicate the peaks of the dark parts of theinterference fringes. The light intensity is particularly high wherebright parts 555 of the three interference fringes 551, 552, 553overlap. Therefore, when a positive photoresist is used, contact holepatterns are formed at the positions corresponding to the parts wherethe parts 555 overlap.

Thus, in the case where the photomask as shown in FIG. 26 is used, animage is formed on the substrate with image intensity corresponding tothe sizes of the main openings 311, 312, 313 and the assist openings321, 322, 323, 324, 325, 326, so that contact hole patterns 491, 492,493 corresponding to the main openings 311, 312, 313 can only be formedin the photoresist 490 (see FIG. 29).

Here, the relation between the position and intensity of the diffractedlight in the projection lens pupil is described.

In FIG. 32, the diffracted light 541 a is a light traveling straight inthe mask, that is, zero-order diffracted light. The diffracted lightcomponents 541 b, 541 c, 541 f are primary diffracted light components.In a commonly used binary mask or attenuated phase-shift mask, thediffracted light components 541 b, 541 c, 541 f have common amplitudeand phase. When the mask pattern is formed by the binary mask or theattenuated phase-shift mask, the amplitude (intensity) A of thediffracted light 541 a in the projection lens pupil and the amplitudesB, C, D of the diffracted light components 541 b, 541 c, 541 f arerepresented by Expressions (25), (26), (27), (28):

$\begin{matrix}{A = {3\left\{ {\gamma + {\left( {1 - \gamma} \right)ɛ_{x}ɛ_{y}}} \right\}}} & (25) \\{B = {\frac{9\left( {1 - \gamma} \right)}{\pi^{2}}{\sin\left( {\pi ɛ}_{x} \right)}{\sin\left( \frac{{\pi ɛ}_{y}}{3} \right)}}} & (26) \\{C = {\frac{9\left( {1 - \gamma} \right)}{2\pi^{2}}{\sin\left( {\pi ɛ}_{x} \right)}{\sin\left( {\frac{2}{3}{\pi ɛ}_{y}} \right)}}} & (27) \\{D = {\frac{3\left( {1 - \gamma} \right)}{\pi}ɛ_{x}{\sin\left( {\pi ɛ}_{y} \right)}}} & (28)\end{matrix}$where ε_(x)=w_(x)/P_(x), ε_(y)=w_(y)/P_(y), and P_(x), P_(y), w_(x),w_(y) are the dimensions of the mask shown in FIG. 30.where γ (a negative value corresponds to the phase-shift mask and 0corresponds to the binary mask) is the complex amplitude transmittanceof a mask light-blocking member (light-blocking region).

<Optimization of Illumination Position>

The shift amount σ of the modified dipole illumination is shifted σx, σywith respect to the center 470 of illumination to satisfy the conditionsin Expressions (23), (24).

In this case, as shown in FIG. 34, the distances r1, r2, r3 of the threediffracted light components 541 a, 541 b, 541 c from the pupil centerare equal to each other. As a result, there is no defocus dependency ofthe interference fringes on the substrate to be calculated later. Thatis, the focal depth is great enough.

<Optimization of Interference Wave Amplitude>

The intensity distribution I (x, y, z) of an interference wave formed onthe substrate by the three diffracted light components 541 a, 541 b, 541c is represented by Expression (29):I(x,y,z)=|A exp(−ik _(a·x))+B exp(−ik _(b·x))+C exp(−ik _(c) ·x)| ²  (29)where A, B, C are the amplitudes of the three diffracted lightcomponents 541 a, 541 b, 541 c shown in FIG. 32, x is a position vectoron the substrate, and ka, kb, kc are wavenumber vectors shown in FIG.35. The wavenumber vectors ka, kb, kc are represented by Expressions(30), (31), (32):

$\begin{matrix}{k_{a} = \left( {S_{x},S_{y},k_{z}} \right)} & (30) \\{k_{b} = \left( {{S_{x} - \frac{2\pi}{P_{x}}},{{Sy} - \frac{2\pi}{3P_{y}}},k_{z}} \right)} & (31) \\{k_{c} = \left( {{S_{x} - \frac{2\pi}{P_{x}}},{{Sy} + \frac{4\pi}{3P_{y}}},k_{z}} \right)} & (32)\end{matrix}$where Sx, Sy are amounts indicating the shift amount σ (σx, σy) of themodified dipole illumination. When this value satisfies Expressions(23), (24), the three diffracted light components 541 a, 541 b, 541 center the substrate at the same angle. Thus, kz is a common z componentof the wavenumber vectors ka, kb, kc.

Expressions (30), (31), (32) are substituted for Expression (29), andthe result is expanded to obtain Expression (33):

$\begin{matrix}\begin{matrix}{{I\left( {x,y,z} \right)} = {A^{2} + B^{2} + C^{2} + {2{AB}\;{\cos\left( {{k_{a} \cdot x} - {k_{b} \cdot x}} \right)}} +}} \\{{2{BC}\;{\cos\left( {{k_{b} \cdot x} - {k_{c} \cdot x}} \right)}} + {2{CA}\;{\cos\left( {{k_{c} \cdot x} - {k_{a} \cdot x}} \right)}}} \\{= {A^{2} + B^{2} + C^{2} + {2{AB}\;{\cos\left( {{\frac{2\pi}{P_{x}}x} + {\frac{2\pi}{3P_{y}}y}} \right)}} +}} \\{{2{BC}\;{\cos\left( {{- \frac{2\pi}{P_{y}}}y} \right)}} + {2{CA}\;{\cos\left( {{{- \frac{2\pi}{P_{x}}}x} + {\frac{4\pi}{3P_{y}}y}} \right)}}}\end{matrix} & (33)\end{matrix}$where the first term on the right side of Expression (33) is a uniformcomponent, the second term is an interference wave produced by theinterference between the diffracted light 541 a and the diffracted light541 b, the third term is an interference wave produced by theinterference between the diffracted light 541 a and the diffracted light541 c, and the fourth term is an interference wave produced by theinterference between the diffracted light 541 b and the diffracted light541 c.

Here, illumination is provided to satisfy the conditions in Expression(26), and thus no component dependent on z appears in Expression (33).This means that the interference fringes are not affected by defocus inthe vicinity of a best focus. That is, the shift amount σ provided byExpressions (23), (24) enables the illumination region to be located atthe optimum position.

The light intensities in the bright part 555 and three kinds of darkparts 556 (dark part 1), 557 (dark part 2), 558 (dark part 3) shown inFIG. 33 are explained in order to consider the contrast of theinterference wave. If the coordinates of the bright part 555 are takenas the origin as shown in FIG. 36, the light intensities in the brightpart 555 and the three kinds of dark parts 556, 557, 558 are provided byExpressions (34), (35), (36), (37):

Intensity of the bright part (555):I(0,0)=A ² +B ² +C ²+2AB+2BC+2CA   (34)

Intensity of the dark part (556):

$\begin{matrix}{{I\left( {\frac{P_{x}}{2},0} \right)} = {A^{2} + B^{2} + C^{2} - {2{AB}} + {2{BC}} - {2{CA}}}} & (35)\end{matrix}$

Intensity of the dark part (557):

$\begin{matrix}{{I\left( {\frac{P_{x}}{3},\frac{P_{y}}{2}} \right)} = {A^{2} + B^{2} + C^{2} - {2{AB}} - {2{BC}} + {2{CA}}}} & (36)\end{matrix}$

Intensity of the bright part (558):

$\begin{matrix}{{I\left( {{- \frac{P_{x}}{6}},\frac{P_{y}}{2}} \right)} = {A^{2} + B^{2} + C^{2} + {2{AB}} - {2{BC}} - {2{CA}}}} & (37)\end{matrix}$

In the case in FIG. 33, three kinds of contrasts C₁, C₂, C₃ can bedefined, as indicated in Expressions (38), (39), (40):

$\begin{matrix}{C_{1} = \frac{{2{AB}} + {2{CA}}}{A^{2} + B^{2} + C^{2} + {2{BC}}}} & (38) \\{C_{2} = \frac{{2{AB}} + {2{BC}}}{A^{2} + B^{2} + C^{2} + {2{CA}}}} & (39) \\{C_{3} = \frac{{2{BC}} + {2{CA}}}{A^{2} + B^{2} + C^{2} + {2{AB}}}} & (40)\end{matrix}$

Suppose conditions where the contrasts C₁, C₂, C₃ are maximized. Thatis, it can be said that the optimum values of the amplitudes A, B, C ofthe three diffracted light components 541 a, 541 b, 541 c are obtainedunder conditions where the minimum values of the contrasts C₁, C₂, C₃are maximized.

Thus, if B=pA and C=qA, then Expressions (38), (39), (40) will beExpressions (41), (42), (43):

$\begin{matrix}{C_{1} = \frac{{2p} + {2q}}{1 + p^{2} + q^{2} + {2{pq}}}} & (41) \\{C_{2} = \frac{{2p} + {2{pq}}}{1 + p^{2} + q^{2} + {2q}}} & (42) \\{C_{3} = \frac{{2{pq}} + {2q}}{1 + p^{2} + q^{2} + {2p}}} & (43)\end{matrix}$

FIG. 37 shows the relation between the minimum values of the contrastsC₁, C₂, C₃ and p, q. It is appreciated from this graph that the minimumvalues of the contrasts C₁, C₂, C₃ are maximized when p=1, q=1. At thispoint, “A=B=C”, so that high contrast (C₁=C₂=C₃=0.8) is obtained.

It is thus apparent that in the case where the diffracted lightcomponents are given as in FIG. 34, a desirable state of image formationis obtained when the amplitudes A, B, C of the three diffracted lightcomponents 541 a, 541 b, 541 c used for image formation are equal toeach other.

<Optimization of Mask Bias and Light-Blocking Portion AmplitudeTransmittance>

The desirable state of image formation is obtained when “A=B=C=D”. Thus,suppose that “B=C”. Expression (44) is obtained in accordance withExpressions (26), (27).

$\begin{matrix}{{\frac{9\left( {1 - \gamma} \right)}{\pi^{2}}{\sin\left( {\pi ɛ}_{x} \right)}{\sin\left( \frac{{\pi ɛ}_{y}}{3} \right)}} = {\frac{9\left( {1 - \gamma} \right)}{2\pi^{2}}{\sin\left( {\pi ɛ}_{x} \right)}{\sin\left( {\frac{2}{3}{\pi ɛ}_{y}} \right)}}} & (44)\end{matrix}$

Expression (44) is expanded to obtain Expression (45):cos(πε_(y)′)=1   (45)

However, it is obvious that Expression (45) is Expression (46):cos(πε_(y)′)≠1   (46)

That is, “B=C” can be said to be an impossible state. It is thereforeimpossible to validate “A=B=C=D”.

Thus, in order to provide a state closest to “A=B=C=D”, the minimizationof Δ (delta) provided by Expression (47) is defined as achieving theoptimum state.

$\begin{matrix}{\Delta = {\frac{{\max\left( {A,B,C,D} \right)} - {\min\left( {A,B,C,D} \right)}}{A + B + C + D}}} & (47)\end{matrix}$

FIG. 38 shows the relation between ε and Δ when a mask bias ε=εx=εy. Itis appreciated from this graph that ε which minimizes Δ increases as theabsolute value of γ (the complex amplitude transmittance of theattenuated phase-shift mask) increases.

FIG. 39 shows the relation between ε and the amplitude A of thediffracted light 541 a. It is appreciated from this graph that the imageis brighter when ε is higher. While the brightness of the image has tobe set in accordance with, for example, a desired throughput, resistsensitivity and the stability of laser luminance, the brightness of theimage can be set by properly selecting a combination of a mask bias andcomplex amplitude transmittance.

As described above, according to the present embodiment, the photomaskhaving the assist openings 321, 322, 323, 324, 325, 326 as shown in FIG.26 is used, and the modified dipole illumination having the luminousregions 451, 452 as shown in FIG. 28 is used. Thus, the highly accuratecontact hole patterns 491, 492, 493 having controlled dimensional errorsas shown in FIG. 29 can be formed even if the pattern is miniaturized(e.g., the minimum pattern pitch is equal to less than λ/NA).

Consequently, when the photomask and modified illumination describedabove are applied to the manufacture of a semiconductor device (exposureof hole patterns), the contact hole CB for bit-line contact to beconnected to the bit line BL can be highly accurately formed in a NANDflash memory, for example, as shown in FIG. 27.

In addition, in the case of the second embodiment described above, theamplitudes of the diffracted light components indicated in Expressions(25), (26), (27), (28) are derived on the basis of the Kirchhoffapproximate model which determines that a mask pattern is formed of aninfinitely thin film. However, when the Kirchhoff approximate model isnot valid, the amplitudes of the diffracted light components can befound by repetitive calculations in such a manner as to change thecomplex amplitude transmittance of the mask and the dimensions of thecontact hole pattern, for example, as shown in FIG. 18.

In particular, when there is no need for a calculation that takes intoaccount the influence of the thickness of the mask, the calculationshown in FIG. 18 has only to be performed using transmittance instead ofthe optical constant of a attenuated film.

Furthermore, six rows of assist openings are provided in the exampledescribed in the above embodiment. This is not limitation. For example,eight or more rows of assist openings may be provided.

Still further, the shape of the main openings and assist openings is notexclusively square and may be, for example, rectangular, circular orelliptic.

Further yet, the shape of the luminous regions of the modifiedillumination is not circular and may be, for example, elliptic.

Further yet, the modified illumination is not exclusively the modifieddipole illumination and can be, for example, modified quadrupoleillumination.

FIG. 40 shows an example of the configuration of modified quadrupoleillumination suitably used for the formation of contact holes forbit-line contact in a NAND flash memory (e.g., a triple zigzagarrangement of holes in a NAND-CB layer).

As shown in FIG. 40, the modified quadrupole illumination has a luminousregion (first luminous region) 651, a luminous region (second luminousregion) 652, a luminous region (third luminous region) 653 and aluminous region (fourth luminous region) 654. These luminous regions651, 652, 653, 654 are enclosed by a nonluminous region 661.

The luminous region 651 and the luminous region 654 as well as theluminous region 652 and the luminous region 653 are provided atsymmetrical positions prescribed by the x- and y-directions with respectto a center 670 of illumination. The center of the luminous region 651and the center of the luminous region 654 are located symmetrically toeach other with respect to the center 670 of illumination. The center ofthe luminous region 652 and the center of the luminous region 653 arelocated symmetrically to each other with respect to the center 670 ofillumination.

In this connection, the distance (σ) between the center 670 ofillumination and a point contained in the luminous region 651 isprovided by σx σy. The distance (σ) between the center 670 ofillumination and a point contained in the luminous region 652 isprovided by σx, −σy. The distance (σ) between the center 670 ofillumination and a point contained in the luminous region 653 isprovided by −σx, σy. The distance (σ) between the center 670 ofillumination and a point contained in the luminous region 654 isprovided by −σx, −σy.

It is ideally desirable that the center of the luminous region 651 becoincident with the point contained therein, the center of the luminousregion 652 be coincident with the point contained therein, the center ofthe luminous region 653 be coincident with the point contained therein,and the center of the luminous region 654 be coincident with the pointcontained therein. In this case, the distances (σ) of the luminousregions 651, 652, 653, 654 from the center 670 of illumination are equalto each other.

In addition, the distance (σ) between the center 670 of illumination andthe point contained in the luminous region 651 is provided byExpressions (48), (49):

$\begin{matrix}{\sigma_{x} = {\frac{\lambda}{18{NA}}\left( {\frac{9}{P_{x}} - \frac{2P_{x}}{P_{y}^{2}}} \right)}} & (48) \\{\sigma_{y} = {- \frac{\lambda}{2P_{y}{NA}}}} & (49)\end{matrix}$where λ is the wavelength of the illumination light, NA is the numericalaperture of the projection lens through which the illumination lightpasses, Px is the pitch of the opening patterns in the bit-linedirection, and Py is the pitch of the opening patterns in the word-linedirection.

In this case, the three diffracted light components 541 a, 541 b, 541 ccan have a state as shown in FIG. 41.

Furthermore, in FIG. 40, for example, the distance (σ) between thecenter 670 of illumination and the point contained in the luminousregion 652 is provided by Expressions (50), (51):

$\begin{matrix}{\sigma_{x} = {\frac{\lambda}{18{NA}}\left( {\frac{9}{P_{x}} - \frac{2P_{x}}{P_{y}^{2}}} \right)}} & (50) \\{\sigma_{y} = {- \frac{\lambda}{2P_{y}{NA}}}} & (51)\end{matrix}$

In this case, the three diffracted light components 541 a, 541 b, 541 ccan have a state as shown in FIG. 42.

As described above, the shape of the modified quadrupole illuminationhaving the luminous regions 651, 652, 653, 654 in the directionsprescribed by the x- and y-directions is set so that three 541 a, 541 b,541 c of the diffracted light components from the photomask pass throughthe projection lens pupil. Thus, the three diffracted light components541 a, 541 b, 541 c reach the substrate through the projection lens, sothat the interference (dark part peaks and bright part peaks ininterference fringes) as shown in FIG. 33 is caused, and an image can beformed on the substrate. As a result, when the photomask in FIG. 26 isused, the contact hole patterns 491, 492, 493 are formed in thephotoresist 490, for example, as shown in FIG. 29.

Furthermore, when the modified quadrupole illumination is employed, itis possible to form in the photoresist 490 randomly arranged independentcontact hole patterns (not shown) in addition to periodic dense holepatterns such as the contact hole patterns 491, 492, 493.

Further yet, the modified illumination is not limited to the modifieddipole illumination and the modified quadrupole illumination describedabove, and can be, for example, modified hexapole illumination havingluminous regions (fifth and sixth luminous regions) 451, 452 andluminous regions (first to fourth luminous regions) 651, 652, 653, 654,for example, as shown in FIG. 43. The luminous regions 451, 452, 651,652, 653, 654 have the same shape and the same dimensions, and areenclosed by a nonluminous region 661.

For example, the distance (σ) between the center 670 of illumination andpoints contained in the luminous region 451, 452 is provided byExpressions (23), (24). The distance (σ) between the center 670 ofillumination and points contained in the luminous region 651, 654 isprovided by Expressions (48), (49). The distance (σ) between the center670 of illumination and points contained in the luminous region 652, 653is provided by Expressions (50), (51).

As described above, the shape of the modified hexapole illuminationhaving the luminous regions 451, 452, 651, 652, 653, 654 is set so thatthree 541 a, 541 b, 541 c of the diffracted light components from thephotomask pass through the projection lens pupil. Thus, the threediffracted light components 541 a, 541 b, 541 c reach the substratethrough the projection lens, so that the interference as shown in FIG.33 is caused, and an image can be formed on the substrate. That is,similarly to the modified quadrupole illumination, in the case where acontact hole for bit-line contact in a NAND flash memory is to beformed, the use of a photomask containing an opening pattern for theformation of an independent contact hole makes it possible not only toform the contact hole for bit-line contact but also to simultaneouslyform, for example, an independent contact hole for peripheral circuitsdifferent in period from the contact hole for bit-line contact.

In addition, the formation of the contact hole for bit-line contact inthe NAND flash memory has been described by way of example in both thefirst and second embodiments. This is however not limitation. Forexample, the present invention is also applicable to the formation ofpatterns for wiring in various semiconductor devices.

Additional advantages and modifications will readily occur to thoseskilled in the art. Therefore, the invention in its broader aspects isnot limited to the specific details and representative embodiments shownand described herein. Accordingly, various modifications may be madewithout departing from the spirit or scope of the general inventiveconcept as defined by the appended claims and their equivalents.

1. A semiconductor device manufacturing method comprising: applyingillumination light from an illumination light source to a photomaskcontaining a mask pattern composed of a transparent region and anontransparent region, and projecting diffracted light components fromthe photomask on a substrate via a projection optical system to form aphotoresist pattern on the substrate, wherein the mask pattern includesa plurality of opening patterns which are the transparent regions, thecenters of the opening patterns being arranged at regular secondintervals on each of a plurality of parallel lines, the plurality ofparallel lines having regular first intervals in a first direction andextending in a second direction perpendicular to the first direction,the centers of the plurality of opening patterns arranged on theadjacent ones of the plurality of parallel lines are displaced from eachother half the second interval; setting the illumination shape of theillumination light source so that three of the diffracted lightcomponents from the photomask pass through the pupil of the projectionoptical system; varying the dimensions of the plurality of openingpatterns and the complex amplitude transmittance of the nontransparentregion in the photomask; and setting the dimensions of the plurality ofopening patterns and the complex amplitude transmittance of thenontransparent region in the photomask so that the three diffractedlight components have equal amplitudes.
 2. The semiconductor devicemanufacturing method according to claim 1, wherein the plurality ofopening patterns are a first plurality of opening patterns and whereinthe mask pattern further includes a second plurality of opening patternswhich are different in dimensions from the first plurality of openingpatterns and which do not form the photoresist patterns on thesubstrate.
 3. The semiconductor device manufacturing method according toclaim 1, wherein the mask pattern shifts the phase of light passingthrough the nontransparent region 180 degrees with respect to lightpassing through the transparent region.
 4. The semiconductor devicemanufacturing method according to claim 1, wherein the illuminationlight source is dipole illumination having a first luminous region and asecond luminous region which are arranged to be displaced from thecenter of the illumination light source in two directions along thesecond direction; and the first luminous region and the second luminousregion include points which are displaced a distance represented byExpression (52) from the center of the illumination light source in thetwo directions along the second direction $\begin{matrix}{\frac{\lambda}{4{NA}}\left( {\frac{1}{P_{y}} + \frac{P_{y}}{P_{x}^{2}}} \right)} & (52)\end{matrix}$ where λ is an exposure wavelength, NA is the numericalaperture of a projection lens, Px is the first interval, and 2Py is thesecond interval.
 5. The semiconductor device manufacturing methodaccording to claim 1, wherein the plurality of opening patterns to whichillumination light from dipole illumination is applied is designed toform contact holes for bit-line contact in a NAND flash memory; and thenumber of the plurality of parallel lines is two.
 6. The semiconductordevice manufacturing method according to claim 1, wherein theillumination light source is quadrupole illumination having a firstluminous region, a second luminous region, a third luminous region and afourth luminous region which are arranged in four regions displaced fromthe center of the illumination light source in the first and seconddirections; and the first to fourth luminous regions include pointswhich are displaced a distance represented by Expression (53) in thefirst direction and a distance represented by Expression (54) in thesecond direction from the center of the illumination light source$\begin{matrix}\frac{\lambda}{2{NAP}_{x}} & (53) \\{\frac{\lambda}{4{NA}}\left( {\frac{1}{P_{y}} - \frac{P_{y}}{P_{x}^{2}}} \right)} & (54)\end{matrix}$ where λis an exposure wavelength, NA is the numericalaperture of a projection lens, Px is the first interval, and 2Py is thesecond interval.
 7. The semiconductor device manufacturing methodaccording to claim 1, wherein the plurality of opening patterns to whichillumination light from quadrupole illumination is applied is designedto form contact holes for bit-line contact in a NAND flash memory; thenumber of the plurality of parallel lines is two; and the mask patternfurther includes opening patterns designed to form independent contactholes for peripheral circuits different in period from the contact holesfor bit-line contact.